Introductory Lectures on Extended Supergravities and Gaugings

In an ungauged supergravity theory, the presence of a scalar potential is allowed only for the minimal N = 1 case. In extended supergravities, a non-trivial scalar potential can be introduced without explicitly breaking supersymmetry only through the so-called gauging procedure. The latter consists in promoting a suitable global symmetry group to local symmetry to be gauged by the vector fields of the theory. Gauged supergravities provide a valuable approach to the study of superstring flux-compactifications and the construction of phenomenologically viable, string-inspired models. The aim of these lectures is to give a pedagogical introduction to the subject of gauged supergravities, overing just selected issues and discussing some of their applications.